Normalization integrals of orthogonal Heun functions
نویسندگان
چکیده
منابع مشابه
Normalization integrals of orthogonal Heun functions
A formula for evaluating the quadratic normalization integrals of orthogonal Heun functions over the real interval 0 ≤ x ≤ 1 is derived using a simple limiting procedure based upon the associated differential equation. The resulting expression gives the value of the normalization integral explicitly in terms of the local power-series solutions about x = 0 and x = 1 and their derivatives. This p...
متن کاملHeun functions versus elliptic functions
We present some recent progresses on Heun functions, gathering results from classical analysis up to elliptic functions. We describe Picard’s generalization of Floquet’s theory for differential equations with doubly periodic coefficients and give the detailed forms of the level one Heun functions in terms of Jacobi theta functions. The finite-gap solutions give an interesting alternative integr...
متن کاملSeries expansion of Wiener integrals via block pulse functions
In this paper, a suitable numerical method based on block pulse functions is introduced to approximate the Wiener integrals which the exact solution of them is not exist or it may be so hard to find their exact solutions. Furthermore, the error analysis of this method is given. Some numerical examples are provided which show that the approximation method has a good degree of accuracy. The main ...
متن کاملQuasi-orthogonal expansions for functions in BMO
For {φ_n(x)}, x ε [0,1] an orthonormalsystem of uniformly bounded functions, ||φ_n||_{∞}≤ M
متن کاملCombinatorial Aspects of Orthogonal Group Integrals
We study the integrals of type I(a) = ∫ On ∏ u aij ij du, depending on a matrix a ∈Mp×q(N), whose exact computation is an open problem. Our results are as follows: (1) an extension of the “elementary expansion” formula from the case a ∈M2×q(2N) to the general case a ∈Mp×q(N), (2) the construction of the “best algebraic normalization” of I(a), in the case a ∈M2×q(N), (3) an explicit formula for ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 1997
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.532062